Interesting question. Purely empirically, it is lift-to-drag ratio you are looking for. If you take this value for given for any particular aircraft, you have directly an answer how more are wings effective. It is ratio of lift to the total drag. Engine needs overcome the drag only.
With L/D equal unity you would need the same thrust as for the vertical take off. But even quite "bad" fixed wing aircraft would have L/D about 5. Gliders or similar aircrafts build with strong focus on aerodynamic can have L/D 50 or more (at least in some narrow range of airspeeds).
So yes, wings are more efficient. About one order of magnitude as a rule of thumb for common aircrafts and optimal airspeed.
Why is your reasoning with air pushed down incorrect is more tricky to explain. I'll start with assumption that, as air passes airfoil, its speed relative to the airfoil is unaltered, only direction changes. (I know air slows down at least because of friction etc., but these are, at least theoretically, avoidable things not related directly to creating the lift. If there is something intrinsically related to lift which makes airflow to change not only direction but speed too, then someone will hopefully correct me here.)
See the image. Airmass moving initially towards airfoil with velocity $\vec{v_0}$ is deflected down by angle $\alpha$. Therefore change in the velocity is $\vec{\Delta v}$. This change can be divided into horizontal and vertical component. To hold aircraft in the air, vertical component has to be equivalent to aircraft weight divided by mass flow over wing. Vertical component is related to horizontal by $$ \Delta v_{\rm horiz}=\Delta v_{\rm vert} \cdot \tan{\alpha\over 2}. $$
So, from this simplistic view, drag would be $\tan\alpha/2$ times lift. More mass flow over the wing (longer wings, higher airspeed) makes possible to keep same lift with lower deflection ($\alpha$), thus less drag due to the generated lift.